cp's OEIS Frontend

A307463 a(n) is the digit after the appearance of n in the decimal numbers of Pi after all the previous natural numbers of n have already appeared except for 0, and without overlap.

%I A307463 #19 Feb 18 2021 09:29:15
%S A307463 4,6,5,6,0,9,5,2,7,2,0,8,3,1,5,0,3,5,4,0,4,4,5,4,2,1,8,3,5,0,5,1,4,5,
%T A307463 6,0,1,9,0,7,0,7,1,6,1,7,9,9,3,6,2,0,9,8,2,4,0,6,8,8,4,2,4,7,4,6,2,7,
%U A307463 5,1,6,0,4,1,4,3,6,3,6,7,6,9,1,5,3,0,4,1
%N A307463 a(n) is the digit after the appearance of n in the decimal numbers of Pi after all the previous natural numbers of n have already appeared except for 0, and without overlap.
%C A307463 All terms appear in the decimal expansion of Pi.
%e A307463 See the first decimal digits of Pi for the examples:
%e A307463 3.(1)4159(2)65(3)589793238(4)62643383279(5)0288...
%e A307463 In parentheses the first appearing of natural numbers after all smaller natural numbers have already appeared.
%e A307463 - FIRST ELEMENT a(1):
%e A307463 For n=1, the first '1' appears in the first decimal place of Pi, and the next decimal digit is '4', so a(1)=4.
%e A307463 - DIGIT POSITION:
%e A307463 For n=4, although the first 4 appears in the 2 decimal place, not all the previous natural numbers of 4 have appeared, so, after 1, 2, and 3 have appeared (in this order), then, a(4) will be the next digit after the next 4. So a(4)=6.
%e A307463 - N WITH MORE THAN 1 DIGIT:
%e A307463 In the decimal digits of Pi: ...50284(10)270193852(11)05...
%e A307463 For n with more than 1 digit, a(n) is, after all the previous natural numbers have appeared, the next digit after all the digits of n have appeared consecutively. Example: a(10)=2, a(11)=0.
%e A307463 - NO OVERLAP:
%e A307463 In the decimal digits of Pi: ...52230825(33)44685035...730359825(34)904...
%e A307463 Example: for n=33, a(33)=4, but, as there is no overlap, the '3' cannot be used again with the '4' for n=34, so a(34) is defined by the next 34: a(34)=9.
%o A307463 (PARI) lista(nn, t=10^5) = {default(realprecision, t); my(d, k=1, v=digits(floor(Pi*10^t))); for(n=1, nn, d=digits(n); while(v[k..k+#d-1]!=d, k++); k+=#d; print1(v[k], ", ")); } \\ _Jinyuan Wang_, Feb 18 2021
%Y A307463 Cf. A000796, A103186.
%K A307463 nonn,base
%O A307463 1,1
%A A307463 _Marc Bofill Janer_, Apr 09 2019
%E A307463 More terms from _Jinyuan Wang_, Feb 18 2021